Left tackle D.J. Humphries has an MCL injury and a dislocated kneecap that will require surgery. Arians wasn't sure when the procedure would take place.
"It's a shame because he was playing really, really well," Arians said.
Safety Tyvon Branch suffered an ACL injury and will have surgery to address it at a later date. He will undergo surgery to repair cartilage in his "locked" right knee on Friday, Arians said.
Tight end Ifeanyi Momah broke his leg and may need reconstructive ankle surgery, Arians said.
The coach said all three players will go on injured reserve.
Despite losing Humphries for the season, his diagnosis was a relief to Arians, who initially believed that the offensive tackle had suffered an ACL injury. The recovery from MCL surgery is less intensive and doesn't take as long. Arians expects Humphries back in three months and said he should be ready for organized team activities in the spring.
Arians also believes the surgery will help repair Humphries' "chronic" MCL issues, which had the third-year veteran wearing a brace on his right knee this season. He missed four games after spraining his right MCL in Week 1.
Arians decided to make the move now instead of in Week 2, after Humphries' first knee injury, because Humphries was expected to return. Now that Humphries' season is over, moving Veldheer to his natural position made sense.
"He'll be our best left tackle now," Arians said.
Arians said he has always felt playing on a short week contributed to injuries, but he added that the statistics show otherwise.
"The statistics say, 'No,'" Arians said. "I look at some of the guys, like D.J. was freaky, Tyvon was freaky, Momah was freaky. So I don't know if it had anything to do with it."